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The name can be somewhat misleading, as the first two highly composite numbers (1 and 2) are not actually composite numbers; however, ... 4,2,1,1,1 9 120 ...
[1] [2] Every positive integer is composite, prime, or the unit 1, so the composite numbers are exactly the numbers that are not prime and not a unit. [3] [4] E.g., the integer 14 is a composite number because it is the product of the two smaller integers 2 × 7 but the integers 2 and 3 are not because each can only be divided by one and itself ...
The first 15 superior highly composite numbers, 2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, 1441440, 4324320, 21621600, 367567200, 6983776800 (sequence A002201 in the OEIS) are also the first 15 colossally abundant numbers, which meet a similar condition based on the sum-of-divisors function rather than the number of divisors. Neither ...
Highly composite numbers: 1, 2, 4, 6, 12, 24, 36, 48, 60, 120, ... A positive integer with more divisors than any smaller positive integer. A002182: Superior highly composite numbers: 2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, ... A positive integer n for which there is an e > 0 such that d(n) / n e ≥ d(k) / k e for ...
Plot of the number of divisors of integers from 1 to 1000. Highly composite numbers are in bold and superior highly composite numbers are starred. ... 120 66 abundant ...
Because 15 is also triangular, 120 is a doubly triangular number. 120 is divisible by the first five triangular numbers and the first four tetrahedral numbers. It is the eighth hexagonal number. The 10th highly composite, [3] the 5th superior highly composite, [4] superabundant, [5] and the 5th colossally abundant number. [6]
1-super abundant numbers are superabundant numbers. 0-super abundant numbers are highly composite numbers. For example, generalized 2-super abundant numbers are 1, 2, 4, 6, 12, 24, 48, 60, 120, 240, ...
[1] The first 15 colossally abundant numbers, 2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, 1441440, 4324320, 21621600, 367567200, 6983776800 (sequence A004490 in the OEIS) are also the first 15 superior highly composite numbers, but neither set is a subset of the other.